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// Establish a range of values on the complex plane
// A different range will allow us to "zoom" in or out on the fractal
// float xmin = -1.5; float ymin = -.1; float wh = 0.15;
float xmin = -2.5; 
float ymin = -2; 
float wh = 4;

size(100, 100);

loadPixels();
  
// Maximum number of iterations for each point on the complex plane
int maxiterations = 200;

// x goes from xmin to xmax
float xmax = xmin + wh;
// y goes from ymin to ymax
float ymax = ymin + wh;
  
// Calculate amount we increment x,y for each pixel
float dx = (xmax - xmin) / (width);
float dy = (ymax - ymin) / (height);

// Start y
float y = ymin;
for(int j = 0; j < height; j++) {
  // Start x
  float x = xmin;
  for(int i = 0;  i < width; i++) {
      
    // Now we test, as we iterate z = z^2 + cm does z tend towards infinity?
    float a = x;
    float b = y;
    int n = 0;
    while (n < maxiterations) {
      float aa = a * a;
      float bb = b * b;
      float twoab = 2.0 * a * b;
      a = aa - bb + x;
      b = twoab + y;
      // Infinty in our finite world is simple, let's just consider it 16
      if(aa + bb > 16.0f) {
        break;  // Bail
      }
      n++;
    }
      
    // We color each pixel based on how long it takes to get to infinity
    // If we never got there, let's pick the color black
    if (n == maxiterations) pixels[i+j*width] = 0;
    else pixels[i+j*width] = color(n*16 % 255);  // Gosh, we could make fancy colors here if we wanted
    x += dx;
  }
  y += dy;
}
updatePixels();

exit();
